Periods and motives in the spectral action of Robertson-Walker spacetimes

Abstract

We show that, when considering the scaling factor as an affine variable, the coefficients of the asymptotic expansion of the spectral action on a (Euclidean) Robertson-Walker spacetime are periods of mixed Tate motives, involving relative motives of complements of unions of hyperplanes and quadric hypersurfaces and divisors given by unions of coordinate hyperplanes.

42 pages

References in corpus (2)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• Rationality of Spectral Action for Robertson-Walker Metrics

Cited by in corpus (2)

• Motives and periods in Bianchi IX gravity models
• Fractality in Cosmic Topology Models with Spectral Action Gravity